Question
Download Solution PDFThe sum of two numbers is 9 and the sum of their squares are 41. The numbers are:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sum of two numbers = 9
Sum of square of their number = 41
Calculation:
Let the two numbers be x and y, so
\(x+y=9\) .... equation 1
\(x^2+y^2=41\) .... equation 2
From equation 1, \(x = 9-y\). Substituting this value in equation 2, we get:
\({{(9-y)^2}+y^2=41}\\ 81+y^2-18y+y^2=41\\ 2y^2-18y+81-41=0\\2y^2-18y+40=0\\ y^2-9y+20=0\\ y^2-5y-4y+20=0\\y(y-5)-4(y-5)=0\\ (y-4)(y-5)=0\\ y-4=0\:or \:y-5=0\\y=4\:or\:y=5\)
Thus, y is either 4 or 5.
Substitute the value of y in equation 1,
- \(x+4=9\\x=5\)
- \(x+5=9\\x=4\)
Thus, x is either 5 or 4.
Therefore, the numbers are 4 and 5.
Last updated on Jul 17, 2025
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